(x+2y+8z) - (6z-2y-x) Can someone explain?

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lemjay's profile pic

lemjay | High School Teacher | (Level 3) Senior Educator

Posted on

`(x+2y+8z)-(6z-2y-x)`

To subtract the expression inside the second parenthesis from the expression inside the first parenthesis, consider the like terms present. These are x & -x, 2y & -2y, and 8z & 6z.

To subtract like terms, subtract the numbers and copy the variable.

`x-(-x)= x+x=(1+1)x=2x`

`2y-(-2y)=2y+2y=(2+2)y=4y`  

`8z-6z=(8-6)z=2z`

Then, write them together. Since all of them are positive, the operation between them would be add.

`(x+2y+8z)-(6z-2y-x)=2x+4y+2z`

Therefore, the given expression

`(x+2y+8z)-(6z-2y-x)`

simplifies to

`2x+4y+2z` .

yamnawaseem's profile pic

yamnawaseem | Student, Grade 11 | (Level 1) eNoter

Posted on

so (x+2y+8z)-(6z-2y-x)

you have to open the second bracket and multiply the number with the negative sign

(x+2y+8z) -6z+2y+x

now open the first bracket

x+2y+8z-6z+2y+x

you add the same variables to get

x+x=2x

2y+2y=4y

and 8z-6z=2z

hence your answer is 2x+4y-2z

atyourservice's profile pic

atyourservice | Student, Grade 11 | (Level 3) Valedictorian

Posted on

(x+2y+8z) - (6z-2y-x)

I know the problem seems difficult but trust me it isnt as scary are it looks.

The first step is to distribute the - in front of the parentheses to the numbers inside: (this will flip the sign of all the numbers)

- (6z-2y-x)

-6z + 2y +x 

now plug this back in:

x + 2y + 8z - 6z + 2y + x

now to make this easier you can move the terms that are alike next to each other, kind of like how 8z and -6z are already next to each other:

x + x + 2y + 2y +8z - 6z

if it makes it easier for you, you can group:

(x + x) + (2y + 2y) + (8z - 6z)

solve:

2x + 4y +2z

rachellopez's profile pic

rachellopez | Student, Grade 12 | (Level 1) Valedictorian

Posted on

(x+2y+8z)-(6z-2y-x)

When given a problem like this you can simply combine like terms. However, you have to be careful with the signs because it is easy to get them mixed up.

Let's start with x. In the first set of parentheses, you have a positive x or 1x. in the second set you have a negative 1x. A positive 1x subtract a negative 1x is equal to 1x + 1x. This gives you 2x.

You'll do the same with the y variables. You are given a 2y in the first parentheses and a negative 2y in the second. 2y - (-2y) is really 2y + 2y, which gives you 4y.

You have 8z in the first parentheses and a positive 6z in the second parentheses. When you subtract a positive 6z from a positive 8z, you just end up with 2z.

After you have combined like terms, all which are positive, you end up with a final answer of 2x + 4y + 2z.

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